From the inimitable xkcd, a comic about relativity in sex:
This rather clever piece of humor is referring to the relativity of simultaneity. According to relativity, time and space are different for observers in different reference frames. Events which are simultaneous in one frame are not necessarily going to be simultaneous in a different frame moving with respect to the first frame. This isn’t just a failure to correct for light travel time either, it’s a genuine geometric effect of spacetime.
So if one person is, er, moving at near the speed of light the effect can be quite pronounced. Simultaneous for one person might not be so simultaneous for another.
What is the same for both observers is the spacetime interval between two events (Let’s say the first event is their pre-coital synchronization of their watches, as any good experimentalists would surely do.) The spacetime interval s2 is defined as the following*:
And the spacetime interval is invariant. For two different observers the time and position of an event may be different, but this combined quantity is necessarily going to be the same for both people. A change in the x, y, and z coordinates of an event (say, as a result of length contraction) is necessarily going to cause a shift of the t coordinate as well.
However, here the “event” in question happens at the same location for both people. The change in location is zero. Therefore the change in time is going to be zero as well. There’s no accumulated relativistic effects to damage the synchronization. Leaving aside the possibility of, uh… falsified data, I’d assume that in fact one of the experimenters messed up the initial clock synchronization. Perhaps forgivable, considering the level of distraction.
*The square of s is generally considered to be the fundamental quantity, not s itself.